We progress to the Elder problem [1]}, which could be considered as a benchmark in the natural convection literature [2]}. The problem's domain and boundary conditions are presented in Figure REF b [3]}, [4]}. As the medium is heated at its lower part, the flow is driven upward by buoyancy. Again, see Table REF , we set \(\mathbf {\mu } = (\mathrm {Ra})\) , and its admissible range of variation is \([350.0, 400.0]\) . We note that as the \(\mathrm {Ra}\)  number considered in this case is relatively high, the flow instability may cause fingering behavior, see Figure REF a-c, first column, [2]}, [4]}. Moreover, the higher \(\mathrm {Ra}\)  value also affect the minimum and maximum \(N^t\)  as its ranges is increased (compared with Example 1) to \([790, 1010]\) . We use \(\mathrm {M} = 40\) , \(\mathrm {M}_\mathrm {v} = 10\) , and \(\mathrm {M}_\mathrm {t} = 10\) . We have in total \(\mathrm {M} N^t = 36110\)  training data points.
